1. Field of the Invention
The present invention relates to a method for calibrating an aircraft's strapdown inertial navigation system based upon data collected during the taxiing mode. More particularly, this invention pertains to an improved method for determining cross-track velocity, and thus east gyro bias error, by taking account of the effect of centripetal acceleration upon error sources.
2. Description of the Prior Art
Aircraft inertial navigation relies upon the integration of data throughout a sequence that is begun when the aircraft is prepared for takeoff and which ends when the aircraft has landed and motion has ceased. The inertial navigation apparatus of an aircraft includes various components, including accelerometers and gyroscopes, that convert the effects of inertial forces into acceleration, velocity and position measurements. The accelerometers determine acceleration forces along three orthogonal sensitive axes and this data is converted, through integrations, into the aircraft's velocity and position. In a strapdown system in which the accelerometers are fixed in relation to the geometry of the aircraft, the gyroscopes that measure the aircraft's attitude also measure that of the accelerometer platforms. The data measured by the gyros is utilized to resolve the accelerometer outputs continuously along the appropriate space axes.
The standard inertial instruments are well-suited for obtaining the necessary flight data in an airborne vehicle. However, important calibration processes take place at the beginning of the flight and prior to the airborne phase to assure that the ultimate measurements of acceleration, velocity and position are substantially free of inaccuracy and bias. Thus, during initial alignment, the precise location and the attitudes of the inertial navigation instruments must be determined and entered into the flight computer, a process that corresponds to the "leveling of the reference platform" that takes place in a non-strapdown or gimballed navigation system.
After initial instrument alignment, the flight computer enters the navigation mode and remains in this mode for the remainder of the flight. While in the navigation mode, the flight computer receives information from the accelerometers and keeps track of the attitudes of the inertial instruments by means of the gyros. Such attitude information is received from the integration of the rate signals received from the gyroscopes.
The initial alignment mode also serves as an opportunity to correct instrument errors. An important error of this sort is the body component of gyro bias error. This error refers to the fixed offset or bias of the angular rate output of the gyros along the aircraft's pitch and roll axes. Unfortunately, in the prior art it has only been possible to partially correct this error.
Conventionally, this problem is addressed by resolving the gyro rates about the pitch and roll axes to a north and east system. A process known as "mini biasing" is then employed during alignment (and prior to taxiing) to correct the gyro components along the northern axis. Unfortunately, the error components along the east axis ("original east gyro bias error") are unobservable during initial alignment. Such non-observability follows from the fact that the initial azimuth determination (i.e. gyrocompassing) utilizes the east component of the gyro outputs to determine azimuth since it is known that the east component of the Earth's angular rate should be zero. Thus, these components are assumed to be correct. That is, the direction of the Earth's rotation rate is employed to determine the initial azimuth of the instrument platform.
FIGS. 1(a) and 1(b) are top plan views of an aircraft during the alignment mode and the taxiing portion of the navigation mode respectively. As shown in FIG. 1(a), at the end of alignment the east component of gyro bias error .epsilon..sub.E.sbsb.o is balanced by the west component of the Earth's angular rate error .delta..OMEGA..sub.w (=.phi..sub.z x.OMEGA..sub.N where .OMEGA..sub.N is the north component of the earth's angular rotation rate) resulting from a residual azimuth error .phi..sub.z. For this reason, velocity errors are not observed until the aircraft changes heading during the taxiing portion of the navigation phase. As shown in FIG. 1(b), when a change of heading occurs, the original east gyro bias error .epsilon..sub.E.sbsb.o rotates with the taxiing aircraft and no longer lies in the east coordinate direction. The west component of the Earth's angular rate error, .delta..OMEGA..sub.w, continues to lie in the west coordinate direction as it is determined by the navigation reference axes rather than by the aircraft body axes.
The absence of a method for determining or, needless to say, correcting the east axis component of gyro error .epsilon..sub.E.sbsb.o can lead to significant difficulties during flight as this error will cause position errors to accumulate through integration. A method for addressing the inherent inability to observe the east component of gyro bias error during the alignment phase is described in a paper of John W. Diesel, "Calibration of a Ring Laser Gyro Inertial Navigation System For Minimum Velocity Error", Fourteenth Biennial Guidance Test Symposium, Central Inertial Guidance Test Facility, Guidance Test Division, 6585th Test Group, Holloman AFB, Vol. II (Oct. 3, 4, 5, 1989) at pages 1--1 through 1-20. That paper describes a system for inferring the original east component of gyro error, .epsilon..sub.E.sbsb.o, through observations made during the post-alignment taxiing portion (i.e. as shown in FIG. 1(b)) of the navigation phase. The method operates upon the relationship between the cross-heading velocity of a taxiing aircraft and the original east component of gyro bias error.
As mentioned earlier, once an aircraft begins taxiing and changes heading, the east component of gyro bias error and the west component of the Earth rotation rate error are no longer balanced, as the original east component of gyro bias error rotates with the body of the aircraft while the west component of the Earth rotation rate error remains aligned with the computed reference system. As a consequence, a net angular rate error begins to build up, resulting in a rate of change or tilting of the computed reference axis system or platform. The tilting of the computed platform generates acceleration error components due to the force of gravity. As the acceleration errors appear, velocity errors develop through integration. Mathematically, the presence of a net angular rate error, once the heading of the aircraft changes, produces a tilt rate of the computed platform. Integration of the tilt rate causes acceleration error components. Further integration of the acceleration error components generates velocity errors, including a cross-track velocity error. Although the north and east velocity errors cannot be observed directly, the cross-track component of velocity error, V.sub.CT, can be observed, and its relationship to the north and east velocity errors is known.
The method described in the above-identified paper relies upon the fact that the velocity in the cross-track direction should be zero as the cross-track direction is, by definition, perpendicular to the true velocity vector. The presence of the north and east velocity errors, however, normally results in a finite value of V.sub.CT. Further, a number of error sources, combine to corrupt the value of V.sub.CT.
Pending U.S. patent application Ser. No. 08/039,725 of John W. Diesel entitled "Method for Calibrating Inertial Navigation Instruments of Aircraft" discusses a method for measuring V.sub.CT that addresses the peculiarly difficult problems presented by one of such error sources, the essentially transient and random .delta.V.sub.n, the error due to lateral and rotational motions of the aircraft while taxiing. Such velocity transients can result from bumps in the runway that affect the landing gear suspension system that can cause the aircraft to roll and to translate both right and left. The resultant sharp velocity spikes are often sufficiently large relative to the cross-heading velocity to overwhelm the error due to the initial east direction gyro bias error.
The pending patent application, property of the Assignee herein, addresses the problems posed by velocity spikes in a method that is based upon recognition of the boundedness of this error source and V.sub.CT. While .delta.V.sub.n can acquire a relatively large value over those brief periods of time as the aircraft "recovers" from transient shocks, its integral is inherently bounded as a taxiing aircraft can be shaken back and forth only so much without breaking the landing gear. It follows from this that the integral of V.sub.CT, the cross-track position error P.sub.CT, is also bounded.
The method disclosed in the pending application does not attempt to estimate the value of the disturbances .delta.V.sub.n. Rather, the impact of that error source upon the optimum estimate of V.sub.CT is evaluated through Kalman filtering. The optimum estimates of V.sub.CT are integrated to produce the cross-track position error P.sub.CT during this process. Kalman gains are computed during this process based, in part, upon the system error model, and are employed to generate optimum estimates of the other parameters that contribute to V.sub.CT.
The value of the above method for determining east gyro bias error is directly dependent upon the quality or accuracy of the estimate of V.sub.CT. This, of course, is impacted by the quality of the error model employed. Insofar as the error model of a system fails to accurately represent the propagation of errors within a system, all error sources will be affected. This, of course, will impact the quality or variance associated with the calculated quantity V.sub.CT, thus directly impacting the east gyro bias error.